Integral dari $$$- 35 x^{9}$$$

Temukan $$$\int \left(- 35 x^{9}\right)\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=-35$$$ dan $$$f{\left(x \right)} = x^{9}$$$:

$${\color{red}{\int{\left(- 35 x^{9}\right)d x}}} = {\color{red}{\left(- 35 \int{x^{9} d x}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=9$$$:

$$- 35 {\color{red}{\int{x^{9} d x}}}=- 35 {\color{red}{\frac{x^{1 + 9}}{1 + 9}}}=- 35 {\color{red}{\left(\frac{x^{10}}{10}\right)}}$$

Oleh karena itu,

$$\int{\left(- 35 x^{9}\right)d x} = - \frac{7 x^{10}}{2}$$

Tambahkan konstanta integrasi:

$$\int{\left(- 35 x^{9}\right)d x} = - \frac{7 x^{10}}{2}+C$$

$$$\int \left(- 35 x^{9}\right)\, dx = - \frac{7 x^{10}}{2} + C$$$A